NBSIR 74-458

Laser Damage in Materials

Albert Feldman, Deane Horowitz; and Roy M. Waxier

Solid State Materials Section

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

March 1974

Final Technical Report

Period Covered: January 1, 1972 to December 31, 1973

ARPA Order No. 2016

Prepared for Advanced Research Projects Agency

Arlington. Virginia 22209

NBSIR 74-458

LASER DAMAGE IN MATERIALS

Albert Feldman, Deane Horowitz, and Roy M. Waxier

Solid State Materials Section

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

March 1974

Final Technical Report

Period Covered: January 1, 1972 to December 31, 1973

ARPA Order No. 2016

Prepared for Advanced Research Projects Agency

Arlington, Virginia 22209

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

LASER DAMAGE IN MATERIALS

Albert Feldman, Deane Horowitz, and Roy M. Waxier

Solid State Materials Section

Inorganic Materials Division

Institute for Materials Research

ARPA Order No 2016

Program Code Number. . 3D10

Effective Date of Contract January 1, 1972

Contract Expiration Date December 31, 1973

Principal Investigator Albert Feldman

(301) 921-2840

The views and conclusions contained in this document

are those of the authors and should not be interpreted as necessarily representing the official policies, either

expressed or implied, of the Advanced Research Projects

Agency or the U. S. Government.
,(
Table of Contents

1. Technical Report Summary 1

1.1 Technical Problem 1

1.2 General Methodology 2

1.3 Technical Results 2

1.4 Department of Defense Implications 3

1.5 Implications for Further Research 3

2. Technical Report 4

2 . 1 Introduction 4

2.2 Self-Focusing Studies in Optical Glasses and YAG . 5

2.3 Relationships Between Self-Focusing Lengths and

Damage, Including Damage in Nd: Doped Laser Glasses 6

2.4 Damage in LiNbOa , Calcite, KDP, and KD*P 9

2.5 Damage in Meodymium-Doped Thoria : Yttrium Oxide

Ceramic Laser Rod 9

3. Publications 10

4. References 11

LASER DAMAGE IN MATERIALS

Abstract

This report suminarizes the study of damage and selffocusing in materials used in Q-switch solid-state laser

systems. In borosilicate crown glass, fused silica, dense flint

glass, and yttrium aluminum garnet, self-focusing appears to be

the main cause of damage. An analysis of damage threshold

measurements with linearly polarized radiation and circularly

polarized radiation suggests that the Kerr effect is the dominant

self-focusing mechanism with a significant contribution to selffocusing from the thermal effect. The electrostrictive effect

is negligible. The damage threshold in Nd: doped laser glasses

appears to be intrinsic. In all the above materials, the damage

threshold for circular polarization is greater than the damage

threshold for linear polarization. In lithium niobate, calcite,

potassium dihydrogen phosphate, and deuterated dihydrogen

phosphate, damage at the lowest levels is caused by inclusions.

Bulk and surface damage thresholds in Nd: doped thoria : yttrium

oxide ceramic are obtained relative to bulk damage thresholds in

several optical materials. Relationships under different geometric

boundary conditions are also derived for solid materials between

the stress-optic coefficients and the electrostrictive

coefficients.

LASER DAMAGE IN MATERIALS

1. Technical Report Siammary

1. 1 Technical Problem

The main objective of this program is the measurement of damage

thresholds and the determination of mechanisms associated with selffocusing in materials used in high-energy pulsed solid-state laser systems.

The materials we have examined are used in the fabrication of optical com- ponents, such as lenses, beamsplitters and mirrors, laser rods, modulators,

Q-switches, and polarizers.

Self-focusing is the main process which leads to intrinsic

bulk damage in laser materials. The damage appears as filamentary

tracks in materials exposed to high-intensity laser radiation. Three

mechanisms have been proposed to explain the effect: electrostriction,

Kerr effect, and thermal self-focusing. By understanding the relative

importance of these mechanisms, we hope to guide the development of

materials with high self-focusing thresholds. The study of self-focusing

can be obscured, however, if extrinsic dcimage processes, such as inclusion

damage, take place.

1.2 General Methodology

Laboratory experiments were conducted to determine the mechanisms

of bulk damage in the following materials:

borosilicate crown glass (BSC 517)

fused silica

dense flint glass (SF 55)

yttrium aluminum garnet (YAG)

five commercial Nd: doped laser glasses

calcite (CaCOa)

potassium dihydrogen phosphate (KDP)

deuterated potassium dihydrogen phosphate (KD*P)

lithium niobate (LiNbOs)

neodymium-doped thoria: yttrium oxide ceramic.

The output of a Q-switched Nd: glass oscillator operating in the TEM^q mode

was focused into the samples. The laser beam was characterized as to

pulse width, pulse time evolution, beam profile, and reproducibility.

1.
Damage sites in the samples were examined to ascertain whether

inclusion damage or self-focusing induced damage was the limiting damage

process. In samples where self-focusing was the principal mechanism of

damage, we performed two different experiments: (1) Damage thresholds

were measured for both linearly and circularly polarized radiation;

(2) damage track positions, which are related to self-focusing lengths,

were measured as a function of laser beam peak power. A theoretical

analysis of the data was made by assuming that the experimental damage

thresholds could be used to determine the self-focusing threshold. The

contributions of the Kerr, electrostrictive , and thermal effects to the

intensity dependent refractive index were theoretically analyzed. The

measurement of damage thresholds for linearly and circularly polarized

radiation provided the necessary and sufficient data from which to estimate

the relative importance of each of the effects to self-focusing. The selffocusing length data were compared to the theoretically predicted values.

1.3 Technical Results

Self-focusing appears to be the principal cause of bulk damage

in BSC 517, fused silica, SF 55, YAG, and Nd: doped laser glass. In all

these materials, we find that the damage threshold for circularly

polarized radiation is greater than the damage threshold for linearly

polarized radiation. A lower bound to the nonlinear index nz and the

contributions of the Kerr effect, electrostriction and the thermal effect

to n2 were obtained from a detailed analysis of the data in BSC 517, fused

silica, SF 55, and YAG. For the pulse width (25 ns) and beam geometry

used, the Kerr effect appears to be the largest contributor to selffocusing with a significant contribution from the thermal effect.

Electrostriction is the smallest of the effects and it would become

negligible for an unfocused beam. Reasonable values of the absorption

coefficient are obtained from the estimated thermal effect. In the

glasses tested, the Kerr effect appears to increase with increasing

refractive index.

Using a focused geometry with a 181-mm focal length lens, we find that damage track position measurements in BSC 517, fused silica,

SF 55, and YAG agree well with self-focusing lengths predicted by theory.

On the other hand, the agreement with theory is poor in the Nd: glasses

and in data obtained with a 362-mm focal length lens in SF 55. The

discrepancy occurs because the position of a damage point on the filament

does not necessarily coincide with a self-focusing point. No significant

difference was found in the damage thresholds among the laser glasses.

We find in calcite, KDP, KD*P, and LiNbOa that inclusions are

the limiting cause of damage. In LiNbOa we also find evidence for selffocusing, but this occurs at higher power levels.

2.
Bulk damage measurements were made in a neodymium-doped

thoria: yttrium oxide ceramic laser rod in cooperation with Charles

Greskovich of the General Electric Corporate Research and Development

Laboratory*. The damage threshold relative to several optical materials

was tabulated.

We have obtained relationships between the stress-optic

coefficients and the electrostriction coefficients for three geometric

situations. Our derivation is based on earlier theoretical work. We

find that the differing results of several authors correspond to solutions

for different geometric boundary conditions.

1 . 4 Department of Defense Implications

The Department of Defense has a need for high-powered solidstate laser systems. Thus it is important (1) to understand the processes

which limit the output power of such systems, (2) to obtain data which

suggest methods for increasing the output power of a given system, and

(3) to verify theories which predict the performance of such systems. We

have come to the following conclusions: (1) In materials for which selffocusing is the dominant mechanism leading to damage, such as glasses,

sapphire, and YAG, the Kerr effect is the dominant self-focusing mechanism.

The Kerr effect increases with increasing refractive index; therefore, for

this type of materials, those having low refractive indices will have

high self-focusing thresholds. (2) The thermal effect can be important

for pulse widths ^ 25 ns or for high repetition rate systems. (3) Inclusion

damage limits the performance of many crystals used presently in modulators

and Q-switches, such as calcite, KDP, KD*P, and LiNbOs. In order to obtain

higher damage thresholds, methods must be found to eliminate the inclusions.

When this is done, self-focusing will then become the limiting process.

1. 5 Implications for Further Research

The interests of the Department of Defense have been shifting

to longer wavelengths in the infrared (10.6 \m for the CO2 laser and 3.8 ym

for the DF laser) . Interest is also expected to shift toward the ultraviolet region even though there are still no important high-power lasers

in this region. Over this wide wavelength range there is a lack of data

on optical materials that could be used for the construction of optical

components . These data include changes of refractive index with temperature

and stress which are important because components subjected to highintensity radiation can undergo a significant change of refractive index

*Research sponsored by ARPA.

3.
due to heat generated by low-level absorption processes. These changes

in index are caused by variations of temperature and by stresses

introduced by temperature gradients. Therefore, measurements of the

refractive index and the change of refractive index with temperature

and stress, in both the infrared and ultraviolet regions of the spectrum,

are worthwhile. Measurements in the infrared of this nature are presently

occurring at the National Bureau of Standards under a joint program with

ARPA.

2. Technical Report

2 , 1 Introduction

The output of high-powered laser systems is limited by the

dcimage occurring in components exposed to the intense electromagnetic

radiation. An understanding of the mechanisms underlying the damage

process is necessary if we are ever to fabricate, in a systematic manner,

materials with high self-focusing thresholds. In the past several years,

significant progress has been made in understanding these underlying

mechanisms. For example, it has been shown that the phase shift due to

Fresnel reflection is the mechanism responsible for the fact that the

damage threshold of an entrance surface is greater than the damage

threshold of an exit surface [1] . In addition, the surface damage

threshold has been significantly increased by appropriate polishing

techniques which eliminate damaging inclusions in the surface region [2,3].

Thus the intrinsic surface damage threshold is thought to be the same as the bulk damage threshold [3]

.

In this report we summarize the conclusions [4-5] reached during

the course of our work over the past two years. We include summaries of our work described in previous reports together with minor modifications.

In all cases the experimental work was done with a Nd: glass Q-switched

laser operating in the TEM^^ mode with a temporal pulse width of 25 ns.

Our work has been concerned with determining the mechanisms

underlying bulk damage. This work includes the study of self- focusing,

which is the main process leading to bulk intrinsic damage in the components

of Q-switched solid-state laser systems. We have estimated the relative

importance of the Kerr effect, electrostriction, and the thermal effect to

self-focusing in materials in which self-focusing is the principal bulk

damage process [5,7,8]. In other materials we found that inclusions are

the limiting cause of damage [6]

.

i

4.
t

2 . 2 Self-Focusing Studies in Optical Glasses and YAG

Damage in the form of filamentary tracks was observed when

1.06 ym laser radiation was focused into samples of BSC 517, fused silica,

SF 55 and YAG. This filamentary damage indicated that self-focusing was

the process leading to damage in these materials. We therefore set out

to determine which of the proposed self-focusing mechanisms, electrostriction, the Kerr effect, or the thermal effect, was the dominant

self-focusing mechanism. By knowing which mechanism predominates, one might then be able to tailor materials with high self-focusing thresholds.

We have estimated the relative contributions of the Kerr effect,

elec'trostriction, and thermal effects to the self-focusing thresholds of

BSC 517, fused silica, SF 55, and YAG from an analysis of damage threshold

data for linearly polarized and circularly polarized radiation. In all

cases, the damage threshold for circular polarization was higher than the

damage threshold for linear polarization. For the beam geometry used, we

conclude that the Kerr effect is the largest effect in all the samples

tested. The thermal effect is also found to be significant, but the

electrostrictive effect is quite small. Both of the latter effects are expected to be insignificant for an individual subnanosecond pulse; however,

because of its integrating nature, thermal self-focusing can be important

in high-repetition-rate laser systems.

The results we have obtained are in qualitative agreement with

the work of others. Absorption coefficients calculated from the estimated

thermal contribution to self-focusing appear to be reasonable for

commercial optical materials.

The assumptions in the analysis tend to minimize the values

we obtain for na (K) . In addition, the thermal contribution may be enhanced

at the expense of n2 (K) . Nevertheless, these considerations do not weaken

but strengthen our basic conclusion, that the Kerr effect is the dominant

self-focusing mechanism. The numbers we calculate indicate that absorption

coefficients of the magnitude present in commercial optical materials

can make a significant contribution to self-focusing.

In this summary we include some modifications to the results

in our earlier report. These modifications have appeared in the

literature [7,8]. In the analysis, in addition to using the damage

threshold data obtained with the 181-mm focal length lens, we also include

data obtained with the 76-mm focal length lens. We then obtain the

critical power for self-focusing

P^j. = {fl - f5)/{ [f^/Pt(2) ] - [ff/P^d)]}. (1)

5.
where P^(l) and P^(2) are damage thresholds obtained with lenses of

focal lengths fi and fz, respectively. If we assume that = Pi from

the theory of Dawes and Marburger [9] , we then obtain a lower bound to

the nonlinear index na. The change of results for the optical glasses

plus a change of laser beam calibration lead to a change in Table II of

reference [5] . The revised table (Table I) is included herewith. Results

for YAG are contained in references [5-7]

.

In analyzing the contribution of electrostriction to selffocusing, we made use of the following relationship between the stressoptic coefficients q and the electrostrictive coefficient Y=

' ^ijkl "^im *^jn Snnkl^'*^' t

where k is the dielectric tensor. A different result was obtained by

Maradudin and Burstein [10] . We showed that the different results are due

to different geometric boundary conditions, much as the polarization

of a solid in an electric field will depend upon the shape of the solid [7]

,

2 . 3 Relationship Between Self-focusing Lengths and Damage, Including

Damage in Nd; Doped Laser Glasses [4,5]

Assuming that a point of damage on a damage track corresponds

to a point of self- focusing, we plotted self- focusing lengths as a function

of peak beam power cind compared the results with the theoretical curve of

Dawes and Marburger [9] . We found surprisingly good agreement between

theory and experiment in BSC 517, fused silica, SF 55, and YAG when we used

the 181-mm focusing lens. There was gross disagreement with theory for

data obtained in five Nd: doped laser glasses. In addition, there was disagreement when radiation was focused in SF 55 with a 362-mm focal length

lens. We propose the following explanation for the discrepancy. For the

data in which there is agreement with theory, the agreement is fortuitous

in that there was an insignificant difference between a point of self-focus

and a point of damage. This difference, in general, may be significant

because the intensity will exceed the damage threshold upstream from a point of self-focus. The self-focus point is where the energy density

is theoretically infinite. An extreme case occurs when damage takes place

without self-focusing or with weak self-focusing. In this case there is no singularity in the energy density. We believe the damage in the

laser glasses to be this latter case. Assuming self-focusing is negligible,

we have calculated the damage threshold of the laser glasses. The results,

which are given in Table II, are based on a focal spot size measured in air.

The spot size is approximately one and one-half times the theoretical size

of a focused beam with a Gaussian profile.

-

^

I

6.
Table I. Contributions of Kerr, electrostrictive , and thermal

effects to self-focusing thresholds^

BSC 517 Fused Silica Dense Flint SF 55

P^(l)^ (MW)

t

0, 47 ± .06 0.65 ± .07 0.124 + .015

P^(2)^ (MW)

t

0. 75 ± .09 1.01 ± .12 0.128 + .015

P • (1)^ (MW)

t

0. 55 ± .07 0.71 ± .08 0.153 + .018

P^(2) (MW) 0. 94 ± .13 1.25 ± .15 0. 170 + .018

P (MW) cr

0. 86 ± .14 1.15 ± .18 0.129 + .018

P ' (MW) or1 _ 149 + + m \J ^ ^

n^ (10 esu) 1. 24 ± .20 0.93 ± .15 8.3 ± 1. 2 -13

n^ (10 esu) 0. 97 ± .18 0.72 ± .12 6.1 ± 0. 8

n2(ES) [10~''"^ esu] 0. 13 0.16 0.68

n^(ES) [lO""""^ esu] 0. 11 0.13 0.68

n^m [10"-^^esu] 0. 80 ± .38 0.56 ± .27 6.4 ± 1. 9

n^ (T) 0. 29 ± .27 0.19 ± .19 1.1 ± 1. 2

a (ciTi ) (3 ± 3) X 10~^ (9 ± 9) X lO"'^ (7 ± 7) X 10-3

The errors occur from the scatter in the data and from the uncertainty

in the power calibration.

obtained with 76-mm-focal-length lens [ 4] . The data have been cor- rected for thermopile calibration and for sample entrance face reflection.

Obtained with 181-mm-focal-length lens.

7.
Table II. Estimated intrinsic damage thresholds for Nd: doped

laser glasses^

Glass Threshold Energy Threshold Energy Density

(mJ) (KJ/cm^)

A 20 + 2 1.3 + 0.3

B 18 + 2 1.2 + 0.3

C 18 + 2 1.2 + 0.3

D 20 + 2 1.3 + 0.3

E 20 + 2 1.3 + 0.3

Data obtained by focusing radiation from a Q-switched Nd: glass

laser (T = 25 ns) with a 181-mm focal length lens. Estimated spot

size radius of the 1/e point of intensity is 21 ym.

8.
2.4 Damage in LiNbOa, Calcite, KDP, and KD*P [6]

An attempt was made to determine the mechanisms for selffocusing in LiNbOa, calcite, KDP, and KD*P. LiNbOs, KDP, and KD*P are electro-optic crystals used in the fabrication of Pockels cells.

Calcite is a common polarizer material. The conclusion we reached

was that inclusions are the principal cause of damage in these crystals,

although filamentary damage caused by self-focusing was observed in

LiNbOa at power levels significantly above the damage threshold.

Energy densities in the vicinity of damage sites in these crystals were

tabulated.

2.5 Damage in Neodymium-Doped Thoria; Yttrium Oxide Ceramic Laser Rod [6]

In cooperation with Charles Greskovitch of the General Electric

Company Corporate Research and Development Center, we conducted bulk and

surface damage threshold measurements on a laser rod constructed of

neodymium-doped thorium: yttrium oxide ceramic. The damage thresholds

relative to several optical materials were tabulated. The thresholds of

this laser rod were lower than the thresholds of all the other materials

tested with the exception of SF 55 glass.

9.
Piabli cations

A. Feldman, D. Horowitz, and R. M. Waxier

"Relative Importance of Electrostriction and the Kerr

Effect to Self-Focusing in Optical Glasses"

Appl. Phys. Lett. 21_, 260 (1972).

A. Feldman, D. Horowitz, and R. M. Waxier

"Relative Contribution of Kerr Effect and Electrostriction

to Self-Focusing" in Laser Induced Damage in Optical Materials : 1972

NBS Special Publication 372

(U.S. Government Printing Office, Washington, D.C., 1972) pp. 92-99.

A. Feldman, D. Horowitz, and R. M. Waxier

"Self-Focusing in Yttrium Aluminum Garnet and Optical Glasses" in

Laser Induced Damage in Optical Materials : 1973

NBS Special Publication 387

(U.S. Government Printing Office, Washington, D.C. , 1973) pp. 26-35.

A. Feldman, D. Horowitz, and R. M. Waxier

"Mechanisms for Self-Focusing in Optical Glasses"

IEEE J. Quantum Electron. QE-9 , 1054 (1973) .

A. Feldman

"Relations Between Electrostriction and the Stress-Optic Effect"

To be published.

A. Feldman, D. Horowitz and R. M. Waxier

"Stress-Optic Measurements in the Infrared"

To be published in Proceedings of the Conference on High-Power

Infrared Window Materials, 1973.

10.
4. References

[1] M. D. Crisp, N. L. Boling, G. Dube , "Importance of Fresnel

Reflections in Laser Surface Damage of Transparent Dielectric

Surfaces," Appl. Phys . Letters _21, 364 (1972).

[2] C. R. Giuliano, "Laser Induced Damage in Transparent Dielectrics:

Ion Beam Polishing as a Means of Increasing Surface Damage

Thresholds," Appl. Phys. Letters 21^, 39 (1972).

[3] D. W. Fradin, Michael Bass, "Comparison of Laser Induced Surface

and Bulk Damage," Appl. Phys. Letters 22_, 157 (1973); D. W.

Fradin and M. Bass, "Studies of Intrinsic Optical Breakdown,"

in Laser Induced Damage in Optical Materials: 1973 , NBS Special

Publication 387 (U. S. Government Printing Office, Washington,

D. C. , 1973) , pp. 225-238.

[4] A. Feldman, D. Horowitz, and R. M. Waxier, "Laser Damage in

Materials," National Bureau of Standards Report 10,894 (July 1972).

[5] A. Feldman, D. Horowitz, and R. M. V7axler, "Laser Damage in

Materials," National Bureau of Standards Report NBSIR 73-119

(February, 1973).

[6] A. Feldman, D. Horowitz, and R. M. Waxier, "Laser Damage in

Materials," National Bureau of Standards Report NBSIR 73-268

(August 1973)

.

[7] A. Feldman, D. Horowitz, and R. M. Waxier, "Self-Focusing in

Yttrium Alumdnum Garnet and Optical Glasses," in Laser Induced

Damage in Optical Materials: 1973 , NBS Special Publication 387

(U. S. Government Printing Office, Washington, D. C. , 1973),

pp. 26-35.

[8] A. Feldman, D. Horowitz, and R. M. Waxier, "Mechanisms for

Self-Focusing in Optical Glasses," IEEE J. Quantum Electron.

QE-9 , 1054 (1973).

[9] E. L. Dawes and J. H. Marburger, "Computer Studies in SelfFocusing," Phys. Rev. 179 , 862 (1969).

[10] A. A. Maradudin and E. Burstein, "Relation Between Photoelasticity, Electrostriction, and First Order Raman Effect in

Crystals of the Diamond Structure," Phys. Rev. 164 , 1081 (1967).

11.

NQS-1 1-IA (REV. 7-7:0

U.S. UEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. 1'UHL1C:A l iON OR Rl-.I'OR V NO. NBSIR 74-458

2. Gov 't Acccs.s ion No.

3. Kci Ipiciu 's Ac Lc.'^>-ion No.

4. '11 1 i.i: .\ND si'irn ri.i-:

Laser Damage in Materials

5. Piibi irat ion Dritt- March 19 74

6. Pi rfortnlng Or/;an i zat ion C o.lc

7. AU'l llOR(S') NBSIR 74-458

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unii No. 3130440

11. Contract /Ciraiit No. 2015/3D10

12. Sponsoring Organization Nanitr and Complete Address (Street, City, Stute, ZIP)

Advanced Research Projects Agency

Arlington, Virginia 22209

Covered

Final Technical Report

1-1-7? to l'?-?'I-73

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES ^

16. ABSTR.ACT (A 200-word or iesa (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it fiere.) This report summarizes the study of damage and self -focusing in materials used in

Q-switch solid-state laser systems. In borosilicate crown glass, fused silica, dense

flint glass, and yttrium aluminum garnet, self-focusing appears to be the main cause of

damage. An analysis of damage^ threshold measurements with linearly polarized radiation

and circularly polarized radiation suggests that the Kerr effect is the dominant selffocusing m.echanism with a significant contribution to self -focusing from the thermal

effect. The electrostrictive effect is negligible. The damage threshold in Ndrdoped

laser glasses appears to be intrinsic. In all the above materials, the damage threshold

for circular polarization is greater than the damage threshold for linear polarization.

In lithium niobate, calcite, potassium dihydrogen phosphate, and deuterated dihydrogen

phosphate, damage at the lov/est levels is caused by inclusions. Bulk and surface damage

thresholds in ndidoped thoria: yttrium oxide ceramic are obtained relative to bulk damage

thresholds in several optical materials. Relationships under different geometric

boundary conditions are also derived for solid materials between the stress-optic

coefficients and the electrostrictive coefficients.

17. KEY W'ORDS (six to twelve entries; alphabetical order; capitalize otily the first letter of the first key word unless a proper

n.imc; separated by semicolons) MDSorption coefficient; damage threshold; electrostriction

;

inclusion damage; intrinsic damage; Kerr effect; laser damage; laser glasses; laser rod

materials; modulator crystals; nonlinear index of refraction; optical glasses; polarizer

materials; self-focusing.

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